Optimal triangular decompositions of matrices with entries from residuated lattices

Result code in IS VaVaI
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Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
Optimal triangular decompositions of matrices with entries from residuated lattices
Original language description
We describe optimal decompositions of an n x m matrix I into a triangular product I 1/4 A / B of an n x k matrix A and a k x m matrix B. We assume that the matrix entries are elements of a residuated lattice, which leaves binary matrices or matrices which con- tain numbers from the unit interval [0,1] as special cases. The entries of I, A, and B represent grades to which objects have attributes, factors apply to objects, and attributes are particular manifestations of factors, respectively. This way, the decomposition provides a model for factor analysis of graded data. We prove that fixpoints of particular operators associated with I, which are studied in formal concept analysis, are optimal factors for decomposition of I in that they provide us withdecompositions I 1/4 A / B with the smallest number k of factors possible. Moreover, we describe transformations between the m- dimensional space of original attributes and the k-dimensional space of factors.We provide illustrative exampl
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BD - Information theory
OECD FORD branch
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Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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